page id: 221 Background Information Euler >  ME 431

ME 431 What to Know

The behavior of physical systems is described by various fundamental laws of nature, such as Newton’s laws of motion, yielding mathematical equations whose solution approximates (or models) the actual behavior of the modeled system. In this class we analyze these mathematical models in hopes of describing the dynamical behavior of the physical system. This course concentrates on the analysis of linear models for the behavior of mechancial systems. We study the forced and transient response of single- and multi-degree-of-freedom systems.

Goals and Objectives

What can we understand about the behavior of mechanical systems in terms of the parameters such as mass, damping, and stiffness? Specifically, how do the structure and parameters of a mechanical system affect its dynamical behavior?


This class requires the following knowledge:
  • Dynamics (basic concepts of kinematics and kinetics)
  • Linear Algebra (vectors, dot products, cross products, etc.)
  • Differential Equations


Put it all together. Use dynamics to model a physical system and differential equations to find the resulting behavior.

In general, to solve any linear differential equation we assume a solution and then “make it fit”. This results in a characteristic equation, whose solution determines characteristics of the system, such as frequency of oscillation and decay rate.

When this class is over, you should understand the following concepts:
  • Degree-of-freedom
  • Single degree-of-freedom systems
    1. Modeling-Momentum balance
    2. Free vibration-assumed solution
    3. Forced vibration
  • Multi degree-of-freedom systems: the behavior of an n-dof system is determined by n 1-dof equations. Compare a single-mode solution with general behavior.
    1. Modeling-Lagrange’s equations
    2. Free vibration
    3. Forced vibration

ABET Outcomes

This course is expected to significantly contribute to ABET outcomes 1, 5, and 11, while addressing outcomes 4, 7, and 9 to a lesser degree:
  1. Apply energy, momentum, continuity, state and constitutive equations
  2. Design and perform laboratory experiments for thermal, fluid and mechanical systems to gather data and test theories
  3. Design thermal, fluid, mechanical and control systems
  4. Participate effectively in same-discipline and cross-disciplinary groups
  5. Identify, formulate, and solve thermal, fluid, and mechanical engineering problems by applying first principles, including open-ended problems
  6. Develop practical solutions for mechanical engineering problems under professional and ethical constraints
  7. Communicate effectively with written, oral, and visual means
  8. Recognize the fact that solutions may sometimes require non-engineering considerations such as art and impact on society
  9. Be prepared for a lifetime of continuing education
  10. Recognize environmental constraints and safety issues in engineering
  11. An ability to use modern modeling and simulation techniques, and computing tools
The complete list of ABET outcomes and objectives for the ME program is also available.

Class Information

Professor: Dr. D. Dane Quinn (
ASEC (North) 313b
Honors Complex 166
Lectures: 4600:431–002 Tu, Th 1:15–2:30pm; Crouse 211
Problem Session: 4600:431–012 Th 4:15&ndash5:05pm; SHS 133
Office Hours Tu, Fr 10:15am-11:15am, and as needed
Text Kelly, S. G., “Mechanical Vibrations: Theory and Applications.”
Cengage Learning, Stamford, CT 2012. ISBN-13: 978-1-4390-6212-8
TA Shihao Wen,